Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact of popular integration methods, we consider a scenario where soft and hard constraints are added to a custom designed deformable linear object. Since the go...

In this paper; we describe a visualization methodfor general logic clauses as the first step of a visualization of logic programs. Since we think inclusion is essential to represent an outline of knowledge, we propose a method based on Euler diagrams to visualize in$rence rules represented as a set of general logic clauses which consist of literals with no variable. We develop a prototype syste...

We study the automorphisms of a graph product of finitely-generated abelian groups W . More precisely, we study a natural subgroup Aut W of AutW , with Aut W = AutW whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition Aut W = (InnW ⋊Out W )⋊Aut W . We also give a number of applications, some of wh...

Given a 3–manifold the second author defined functions δn : H (M ;Z) → N, generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non– commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.

We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These area-proportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing area-proportional Ven...

We present the OSp(2, 2|6) symmetric algebraic curve for the AdS 3 /CF T 4 duality recently proposed in arXiv:0806.1218. It encodes all classical string solutions at strong t'Hooft coupling and the full two loop spectrum of long single trace gauge invariant operators in the weak coupling regime. This construction can also be used to compute the complete superstring semi-classical spectrum aroun...

In this paper, stochastic age-structure population system with jump are studied. It is proved that the semi-implicit Euler approximation solutions converge to the analytic solution for the stochastic age-structured population system with Poisson jump. The analysis use ˆ Ito s ′ formula, Burkholder-DavisGundy's inequality, Gronwall's lemma and some inequalities for our purposes.

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated SemiLagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. The new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection meth...